72=2.5(5c+12)3c

Solution for 72=2.5(5c+12)3c equation:

Simplifying
72 = 2.5(5c + 12) * 3c

Reorder the terms:
72 = 2.5(12 + 5c) * 3c

Reorder the terms for easier multiplication:
72 = 2.5 * 3c(12 + 5c)

Multiply 2.5 * 3
72 = 7.5c(12 + 5c)
72 = (12 * 7.5c + 5c * 7.5c)
72 = (90c + 37.5c2)

Solving
72 = 90c + 37.5c2

Solving for variable 'c'.

Reorder the terms:
72 + -90c + -37.5c2 = 90c + -90c + 37.5c2 + -37.5c2

Combine like terms: 90c + -90c = 0
72 + -90c + -37.5c2 = 0 + 37.5c2 + -37.5c2
72 + -90c + -37.5c2 = 37.5c2 + -37.5c2

Combine like terms: 37.5c2 + -37.5c2 = 0.0
72 + -90c + -37.5c2 = 0.0

Begin completing the square.  Divide all terms by
-37.5 the coefficient of the squared term: 

Divide each side by '-37.5'.
-1.92 + 2.4c + c2 = 0

Move the constant term to the right:

Add '1.92' to each side of the equation.
-1.92 + 2.4c + 1.92 + c2 = 0 + 1.92

Reorder the terms:
-1.92 + 1.92 + 2.4c + c2 = 0 + 1.92

Combine like terms: -1.92 + 1.92 = 0.00
0.00 + 2.4c + c2 = 0 + 1.92
2.4c + c2 = 0 + 1.92

Combine like terms: 0 + 1.92 = 1.92
2.4c + c2 = 1.92

The c term is 2.4c.  Take half its coefficient (1.2).
Square it (1.44) and add it to both sides.

Add '1.44' to each side of the equation.
2.4c + 1.44 + c2 = 1.92 + 1.44

Reorder the terms:
1.44 + 2.4c + c2 = 1.92 + 1.44

Combine like terms: 1.92 + 1.44 = 3.36
1.44 + 2.4c + c2 = 3.36

Factor a perfect square on the left side:
(c + 1.2)(c + 1.2) = 3.36

Calculate the square root of the right side: 1.833030278

Break this problem into two subproblems by setting 
(c + 1.2) equal to 1.833030278 and -1.833030278.

Subproblem 1
c + 1.2 = 1.833030278

Simplifying
c + 1.2 = 1.833030278

Reorder the terms:
1.2 + c = 1.833030278

Solving
1.2 + c = 1.833030278

Solving for variable 'c'.

Move all terms containing c to the left, all other terms to the right.

Add '-1.2' to each side of the equation.
1.2 + -1.2 + c = 1.833030278 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + c = 1.833030278 + -1.2
c = 1.833030278 + -1.2

Combine like terms: 1.833030278 + -1.2 = 0.633030278
c = 0.633030278

Simplifying
c = 0.633030278

Subproblem 2
c + 1.2 = -1.833030278

Simplifying
c + 1.2 = -1.833030278

Reorder the terms:
1.2 + c = -1.833030278

Solving
1.2 + c = -1.833030278

Solving for variable 'c'.

Move all terms containing c to the left, all other terms to the right.

Add '-1.2' to each side of the equation.
1.2 + -1.2 + c = -1.833030278 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + c = -1.833030278 + -1.2
c = -1.833030278 + -1.2

Combine like terms: -1.833030278 + -1.2 = -3.033030278
c = -3.033030278

Simplifying
c = -3.033030278

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {0.633030278, -3.033030278}